Cut the flaps off one side of the box. Save the flaps for later. Cut down the sides of the box until they are only 4 inches high. Pick the longest side of the box, and cut it down to a height of about 1 inch. These heights are only suggestions, but you want one side much shorter than the other three, so water has somewhere to flow.
Place the box on the ground, with the bottom of the box (the side that still includes the flaps) facedown. Use the saved flaps to separate the box into three equal-sized areas. Each compartment should be open on the side of the box with the 1-inch wall. Add 1 inch of soil to each compartment, pushing the soil down into the box firmly. Leave the first compartment alone. Cover about half of compartment two with peat moss. Cover all of compartment three with peat moss. Use a brick or other flat object to prop up one end of the box, to create a sloping surface.
Pour water slowly across the three sections, using a pitcher or other container. Encourage the children to catch the water that runs off the compartments and examine the amout of soil lost during this simulated rainstorm. As an extra step, scatter some small gravel on one side of a compartment and see if that makes a difference with the rate of erosion.
A more ambitious version of this project can be built using wood to construct a more permanent box. Use the same dimensions, then leave the box and its contents outside to observe the effects of rain and wind.